Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States

Description

Cover Half Title Series Page Title Page Copyright Page Dedication Table of Contents A Note about the 20th Anniversary Edition Author’s Preface to the 20th Anniversary Edition Series Editor’s Introduction to the 20th Anniversary Edition: What Makes a Classic? Author’s Preface to the 2010 Edition Series Editor’s Introduction to the 2010 Edition Foreword Acknowledgments Introduction 1. Subtraction With Regrouping: Approaches To Teaching A Topic The U.S. Teachers’ Approach: Borrowing Versus Regrouping The Chinese Teachers’ Approach: “Decomposing a Higher Value Unit” Discussion Summary 2. Multidigit Number Multiplication: Dealing With Students’ Mistakes The U.S. Teachers’ Approach: Lining Up Versus Separating Into Three Problems The Chinese Teachers’ Approach: Elaborating the Concept of Place Value Discussion Summary 3. Generating Representations: Division By Fractions The U.S. Teachers’ Performance on Calculation The Chinese Teachers’ Performance on Calculation The U.S. Teachers’ Representations of Division by Fractions The Chinese Teachers’ Approach to the Meaning of Division by Fractions Discussion Summary 4. Exploring New Knowledge: The Relationship Between Perimeter And Area How the U.S. Teachers Explored the New Idea How the Chinese Teachers Explored the New Idea Discussion Summary 5. Teachers’ Subject Matter Knowledge: Profound Understanding Of Fundamental Mathematics A Cross-Topic Picture of the Chinese Teachers’ Knowledge: What Is Its Mathematical Substance? Knowledge Packages and Their Key Pieces: Understanding Longitudinal Coherence in Learning Elementary Mathematics as Fundamental Mathematics Profound Understanding of Fundamental Mathematics Summary 6. Profound Understanding Of Fundamental Mathematics: When And How Is It Attained? When Is Profound Understanding of Fundamental Mathematics Attained?: What the Preteaching Groups Knew About the Four Topics Profound Understanding of Fundamental Mathematics: How It Is Attained Summary 7. Conclusion Address Teacher Knowledge and Student Learning at the Same Time Enhance the Interaction Between Teachers’ Study of School Mathematics and How to Teach It Refocus Teacher Preparation Understand the Role That Curricular Materials, Including Textbooks, Might Play in Reform Understand the Key to Reform: Whatever the Form of Classroom Interactions Might Be, They Must Focus on Substantive Mathematics Appendix References Bridging Polarities: How Liping Ma’s Knowing and Teaching Elementary Mathematics Entered the U.S. Mathematics and Mathematics Education Discourses Response to “Bridging Polarities: How Liping Ma’s Knowing and Teaching Elementary Mathematics Entered the U.S. Mathematics and Mathematics Education Discourses” New to the 20th Anniversary Edition: A Critique of the Structure of U.S. Elementary School Mathematics Index